Calculus Examples

$f' (x) = \sin (\frac{π}{4})$

Step 1

The function $f (x)$ can be found by evaluating the indefinite integral of the derivative $f' (x)$ .

$f (x) = \int f' (x) d x$

Step 2

Apply the constant rule.

$\sin (\frac{π}{4}) x + C$

Step 3

Rewrite $\sin (\frac{π}{4}) x + C$ as $\frac{\sqrt{2}}{2} x + C$ .

$\frac{\sqrt{2}}{2} x + C$

Step 4

The function $f$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$f (x) = \frac{\sqrt{2}}{2} x + C$